In a drilling machine including an electric drill with a positioning member for fixing it to a workpiece, such as an electromagnetic base, and a front member, for instance, an annular cutter, there is a larger torque as compared with a drilling machine having a twist drill. Consequently, when an abnormally increased load is applied on the annular cutter, breakage of the cutting edge or burning-out of the motor for driving the electric drill may occur. Thus, the operator has to handle such a drilling machine while paying constant attention so as to prevent a larger load from being applied on the annular cutter. However, difficulties are still encountered in reducing the occurrence of such breakage or burning-out of the motor, since visual identification of loading demands sophisticated skill. In this respect a great deal of room is left for improvement. To add to this, drilling should be shut off immediately upon the completion of the drilling step to prevent breakage of the annular cutter and to save power. A great deal is left to be desired in this regard.